Answer
The volume of the cylinder is\[21\pi \text{ y}{{\text{d}}^{3}}\text{ or 66y}{{\text{d}}^{3}}\].
Work Step by Step
The diameter and height of the cone are 6yd and 7yd, respectively. The volume of the cone will be computed by multiplying the square of the radius with the height and finally multiplying the resultant with the value of pie. Now, multiply the final resultant figure with one-third to get the volume of a right circular cone.
Firstly, compute the radius of the cone using the equation:
\[\begin{align}
& \text{Radius}=\left( \frac{1}{2}\times 6 \right)\text{yd} \\
& =3\text{yd}
\end{align}\]
Compute the volume of the cone using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cone }\left( V \right)=\frac{1}{3}\left( \pi {{\left( 3\text{ yd} \right)}^{2}}7\text{ yd} \right) \\
& =\frac{1}{3}\left( \pi \right)9\text{y}{{\text{d}}^{2}}\times 7\text{ yd} \\
& =\frac{1}{3}\left( 63\pi \right)\text{y}{{\text{d}}^{3}}
\end{align}\]
Further simplify it to get:
\[\begin{align}
& \text{Volume of the Cone }\left( V \right)=\frac{1}{3}\left( 63\pi \right)\text{y}{{\text{d}}^{3}} \\
& =21\pi \text{ y}{{\text{d}}^{3}} \\
& =66\text{ y}{{\text{d}}^{3}}
\end{align}\]
